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I know from a theory that if $X_1,X_2,...,X_n$ be iid from continuous Uniform(0,1), then k-th order statistic $X_{(k)}$ is Beta$(k,n-k+1)$.

Now, $X_1,X_2,...,X_n$ be iid from continuous Uniform$(a,b)$, where $a=\mu-\sqrt{3}\sigma$ and $b=\mu+\sqrt{3}\sigma$. I would like to know that what is the distribution of $X_{(k)}$? Can I apply the theorem?

kjetil b halvorsen
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aris
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    A Uniform (a,b) variable X can be written as a+(b-a)U, where U is Uniform (0,1). This should solve your problem. – Xi'an Nov 01 '17 at 15:18
  • @Xi'an Could you please explain for X=a+(b-a)U? Many thanks. – aris Nov 01 '17 at 15:26
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    What I wrote is called an hint. You now have to work out the solution. – Xi'an Nov 01 '17 at 15:37
  • See https://stats.stackexchange.com/questions/4659/relationship-between-binomial-and-beta-distributions/4684#4684. – whuber Nov 01 '17 at 15:40

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